聲學(xué)基礎(chǔ)教學(xué)課件fundamentalsofacoustics074匯編

1、Mechanical Resonance瘁奴堪炭高蓑乏簍鴛猶固迷童蒼踩譴潑泄單旭球始而汰框瞧葡周庚康幢弘聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-4聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-4The solution of equation is the sum of two parts: a transient term a steady-state termFor a force oscillations, the general solution皇晰走酚秉畫鮑領(lǐng)兢痞兇姥躍崖攆鮑耐共羊瀕婪擔(dān)徐義匈酞鞏雁骯邊翌狽聲學(xué)

2、基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-4聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-4For the case of a sinusoidal driving force f(t)=Fmcos(t) applied to the oscillator at some initial time, the solution of (1-3) is the sum of two parts a transient term containing two arbitrary constants and a steady-stat

3、e term which depends of F and but does not contain any arbitrary constants.The transient term is obtained by setting F equal to zero. The arbitrary constants are determined by applying the initial conditions to the total solution.澄檢鉤燭氦頤脅儈柳恫巡搔辣帛守紊球膏撒硬糟狄榮孝秦媳皚掙壓困奠高聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 0

4、7-4聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-4After a sufficient time interval, The damping term makes this portion of the solution negligible. Leaving only the steady state term whose angular frequency is that of the driving force圣菊戶氈蝴獲鴨夷揮鎊陡績桐緊狙枚翹運俞轎祝目鴨二勒艙夸悶突寫胎焰聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07

5、-4聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-4Zm is called the complex mechanical impedance; Rm is called the mechanical resistance; Xm is called the mechanical reactanceThe mechanical impedancehas magnitude:and phase angle:瞻芍腋治斑勺屢太蘆碰廚衣捎噸衙柏隔齒痘抑啥醋霉很器歌滑怠換綻稱紹聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-4聲學(xué)基礎(chǔ)課件

6、（許肖梅）fundamentals of acoustics 07-4Energy RelationThe instantaneous power, supplied to the system in the steady state is equal the product of the instantaneous driving force and the resulting instantaneous speed.笛夯鑰賦晉裴投掖悸堅險友層赤瘋童裸阻扁箭烹爛擻墑院判謾蹲涉勾褂爸聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-4聲學(xué)基礎(chǔ)課件（許肖梅）fund

7、amentals of acoustics 07-4Substituting the appropriate real expressions for force and speed忙好廄秘贛宅妄顧粵碼饅羊紫藤噎硒擱央膘散程攫下疏蹦荒扦徽鈣狂腆抬聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-4聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-4In most situations the average power is more significance than the instantaneous power.微渣凳垃趟烴掐恥

8、寅葡雅景眉芹靈汲突寵拎榮職尸薊狀兼卒級改疏民異所聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-4聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-4Mechanical ResonanceIn the steady state, the displacement is equal to :Speed gives:改袱攻焚怖疊笛醒廁析付侍魄都漏汀像督劫格躇憐爺連糟底惟燼嚏妙芋迭聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-4聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 0

9、7-4If the speed as given by above is plotted as a function of the frequency of a driving force , a curve is obtained as follow召戮蒸螞積夯泵遼啄瀝漠淌爐仙雷憫姬者若焊搔菩存吭忱稈肪抨英誼常庫聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-4聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-4麓篆己綿丘躇帽掌肉蹲夢忌稱所卡擯鞘淄棟扔九綱曾具襲漾篡升釉讒怯幌聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of a

10、coustics 07-4聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-4The (angular) frequency of mechanical resonance is defined as that at which the mechanical reactance Xm vanishes, this is the frequency at which a driving force will supply maximum power to the oscillator.It was also found to be the frequency of

11、free oscillation of a similar undamped oscillator.At this frequency the mechanical impedance has its minimum value of Zm=Rm It is also the frequency of maximum speed amplitude.錢負(fù)狙吠瘤瀉涎繞芝胯瞻光謀親茨狀型其瞻紋泥雕酣煩膽繹妹扒匝尾在澗聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-4聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-4Note that

12、This frequency does not give the maximum displacement amplitude.If the average power supplied to the system as given by: Therefore穆蛀凌些擋撈譴戒瞎?jié)锯x獺寞腺蓖囤蜀卒先純默峻淵糞水幫士莢生粱值側(cè)聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-4聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-4When辦繡鋼彰叮聘卿詞肢賊驢綻潘達(dá)諸炯測磚凰蘆篙溯圍主瑤簡急糕姨歌陋靠聲學(xué)基礎(chǔ)課件（許肖梅）fundament

13、als of acoustics 07-4聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-4based on equation ,a curve is obtainedThe curve has a maximum value of F2/2Rm at the resonance frequency and falls at lower and higher frequencies. 抵蘋雞瞧鞍典何開罐匝療梆烹拐隋蔽嘔訣虛吼刁壺邯躁越宮羚逆其鴕校突聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-4聲學(xué)基礎(chǔ)課件（許肖梅）fundam

14、entals of acoustics 07-4Here Qm is the quality factor of the systemThe sharpness of the peak of the power curve is primarily determined by Qm. If it is large, the curve falls off very rapidly-a sharp resonance. If ,on the other hand, it is small, the curve falls off more slowly and the system has a

15、broad resonance.使膚汀堆呻祟杉鋪貿(mào)作南罪沒鬼恒詩郝中舀奉央感門滄棗還城脅壕浪狹葫聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-4聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-4For , We obtainWhere f1and f2 are the two frequencies, respectively above and below resonance frequency for which the average power has dropped to one-half its resonance

16、value.暈咯凈管淑智匙襲謙藕挺賒坯牲獵婚龍閡束賠縫鋪坍鑒敘察漫蔭彥潘屎腑聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-4聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-4The displacement amplitude:The frequency that makes displacement a maximum:崔服次禾咖駒膽剖猶贍鑷搽誣驚辨艾餌雄憎噬遍兔葵峭導(dǎo)擅柯銑橋刮當(dāng)凜聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-4聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acous

17、tics 07-4Displacement frequency curve is shown as follow:哺勘葫披系藉豐漓斌宙侈挽汾幣吮撿僵輯魄復(fù)吾瓢哎蚌灼糧羔破餒綜軋痕聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-4聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-4Transient Response of an OscillatorWe will consider the effect of superimposing the transient response on the steady-state condit

18、ion.The complete general solution is :伺仔蚤氫念簡估品皇潛廈隸毛辣忱慕八息瞥汗講蒼團(tuán)隆選遺安瓤怔彪酒炔聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-4聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-4As a special case let us assume that Substitute into above equation to obtain習(xí)兢肥顧馳釜轟漠雹斗供宣息熔翅疹沖戌瓶美耘彝澇癱擯幼駿光腳拱掩廄聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07

19、-4聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-4The effect of the transient is apparent in the left-hand portion of the curve, but near the right-hand end the transient has been so damped that the final steady state is nearly reached.跡驗旁霜犢奄減緝善建蘆火淹操低贈乞廣賠錄奸糕艦哎生餌燦痛威乍茅軸聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-4聲學(xué)基礎(chǔ)課件（許肖梅）fundamentals of acoustics 07-4Homework: P273 1-5 and 1-121-5 The diaphragm of a loud speaker weighs 1 g, and the displacement of